There are competitors, just in terms of the major long trails of the USA, there is the Pacific Crest(PCT) and the Continental Divide (CDT) those three make up the Triple Crown of long distance hiking in the USA ( http://aldhawest.org/triple-crown/ )

And several others; https://en.wikipedia.org/wiki/Long-distance_trails_in_the_Un...

I'd say the PCT is its closest competitor as the PCT is considerable well marked, but its an easier trail grade to hike(and on the other side of the country)

If you want remoteness and untouched wilderness, I went days without seeing another person (and some hikers can go weeks depending on the year) on the CDT at all though some extraordinarily beautiful locations. Of course its not as defined as the PCT or AT(compass navigation is requires as the trail doesn't always exist)

The thing about the AT is it is the most accessible of any of the major trails, I've heard that about half the US population is within a 1day drive of some point of the trail.